A former PhD student has been sentenced to life in prison for the kidnap and murder of a Chinese graduate student at the University of Illinois.
Brendt Christensen received the life term after a jury was unable to reach a unanimous verdict on whether he should be given the death penalty.
Christensen, 30, abducted Yingying Zhang on the university campus in June 2017 before beating her to death with a baseball bat and decapitating her.
Her remains have never been found.
Ms Zhang's parents and fiance had attended the five-week trial in Peoria, south-west of Chicago.
The proceedings have been followed closely in China, which sent consular officials to Thursday's hearing.
Handing down the sentence of life in prison without the possibility of release, US District Judge James Shadid said Christensen's actions were "an inexplicable act of violence".
He said the Zhang family might never learn where their daughter's remains rested.
"Whatever self-centred opinion you have of yourself, when you are taken out of here today by the United States marshals, to wait for that lonely, isolated and cold deathbed that follows your natural life in prison, maybe, just maybe, the moment will strike you to pick up paper and pen and write 'I'm sorry' to Mr and Mrs Zhang," he said, according to the Chicago Tribune.
Christensen did not speak during the hearing.
Afterwards, Zhang's father, Ronggao Zhang, said the family would "not have peace or closure" until her remains were found.
"If you have any humanity left in your soul, please help us end our torment," said a family statement addressed to Christensen.
John Milhiser, US attorney for the Central District of Illinois, told a news conference that efforts to find the student's remains would continue.
The court had heard how Zhang, 26, disappeared in Champaign, a city about 135 miles (200km) south of Chicago, barely two months after coming to the US.
She had been on her way to sign a lease for an apartment when Christensen posed as an undercover police officer to coax her into his car. Surveillance footage captured the abduction.
The trial was told that Christensen had approached another young woman earlier on the same day but she refused to get into his vehicle.
Christensen's former girlfriend, Terra Bullis, testified that he had confessed to the murder to her while they attended a vigil for the missing student.
Ms Bullis said she agreed to wear a hidden microphone for the FBI in order to record her conversations with Christensen.
Jurors heard the secretly taped audio in which Christensen describes in detail how he sexually assaulted Zhang, killed and decapitated her. He also told of her "valiant" attempt to fight back.
Although Illinois has abolished capital punishment, Christensen was charged in federal court, which had made him eligible for the death penalty.
The case has been closely watched in China. On Chinese social media site Weibo, the hashtag "Murderer of Zhang gets life imprisonment" received over 400 million views.
Many were enraged that Christensen did not receive the death penalty.
"A great injustice has been done," said one commenter on Weibo. "The sentence shows the inadequacy of the jury."
"The jury has given Christensen a chance to escape death," said another commenter. "Unfortunately, Zhang never got such a chance."